| TAOP52 |
Introduction to Operations Research, 4 ECTS credits.
/Optimeringslära, grundkurs/
For:
I
Ii
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Prel. scheduled
hours: 50
Rec. self-study hours: 57
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
Optimization deals with mathematical theory and methods aiming at analyzing and solving decision problems that arise in technology, economy, medicine, etc. The course gives a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems. After the course, the student shall:
- be able to explain important classes of ptimization problems and to be able to classify them according to their properties, into, for example, linear and nonlinear problems
- model mathematical models of simple optimization problems
- be able to explain basic concepts, such as, for example, local and global optimality, convexity, weak and strong duality
- have knowledge about and be able to apply basic theory for some common types of optimization problems, such as, for example, duality theory for linear optimization problems, and have knowledge about and be able to use optimality conditions, such as, for example, KKT-conditions, to determine the optimality of a given solution
- be able to explain and to apply basic principles for solving some common types of optimization problems, such as, for example, the simplex method for linear problems
- be able to estimate the optimal objective value through lower and upper bounds
- be able to use commonly available software for solving optimization problems of standard type
- have some knowledge of practical applications of optimization
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, Linear Algebra.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Operations Research, extended course, Economic Analysis: Economic Theory, Economic Analysis: Decision- and Financial Methodology, Production and Operations Management
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Organisation:
Lectures which include theory, problem solving and applications. Exercises which are intended to give individual training in problem solving. A laboratory course with emphasis on modelling and the use of optimization software.
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Course contents:
Linear programming: the simplex method, sensitivity analysis, duality.
Nonlinear programming, convex functions and sets, iterative methods for problems with or without constraints, optimality conditions (Karush-Kuhn-Tucker conditions)
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Course literature:
Lundgren J, Rönnqvist M, Värbrand P: Optimeringslära. Studentlitteratur (2003, reviderad 2008), ISBN: 9789144053141.
Henningsson M, Lundgren J, Rönnqvist M, Värbrand P: Optimeringslära övningsbok (2010), ISBN: 9789144067605
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Examination: |
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Written examination
Labratory work
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3 ECTS
1 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Nils-Hassan Quttineh
Course Syllabus in Swedish
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